31 citations · 34 across the 5 of their papers we have counts for
6 papers · 1 filter
Computing Spectral Properties of Differential Operators on Surfaces
Gustav Conradie, Matthew J. Colbrook, Daniel Fortunato
Computing spectra of differential operators on surfaces is crucial in many applications, ranging from medical image analysis to nanoscale quantum structures. However, discretizatio…
Corner cases of the tau method: symmetrically imposing boundary conditions on hypercubes
Keaton J. Burns, Daniel Fortunato, Keith Julien +1
Polynomial spectral methods produce fast, accurate, and flexible solvers for broad ranges of PDEs with one bounded dimension, where the incorporation of general boundary conditions…
A high-order fast direct solver for surface PDEs
Daniel Fortunato
We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincaré-Steklov method. The method takes a…
The ultraspherical spectral element method
Daniel Fortunato, Nicholas Hale, Alex Townsend
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincaré-Steklov scheme for solving second-order linear partial differ…
Efficient operator-coarsening multigrid schemes for local discontinuous Galerkin methods
Daniel Fortunato, Chris H. Rycroft, Robert Saye
An efficient -multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the…
Fast Poisson solvers for spectral methods
Daniel Fortunato, Alex Townsend
Poisson's equation is the canonical elliptic partial differential equation. While there exist fast Poisson solvers for finite difference and finite element methods, fast Poisson so…